Systems and methods for suppressing turbulence in pipe and channel flows - Patents.com

Abstract

Systems and methods for actively and passively suppressing the transition of a fluid flow from laminar to turbulent flow in conduits for fluid transport, including pipes, channels, and partially confined passages. Examples include implementation of a turbulence model to predict a turbulent transition mode of a fluid in the conduit, and systems and methods for modifying the fluid in the conduit to reduce or suppress the predicted turbulent transition mode, thereby preventing or delaying the transition of the fluid flow from laminar to turbulent flow. Examples include active systems for introducing disturbances into the fluid flow that counteract, absorb, or reduce the predicted turbulent transition mode. Examples include conduit liners configured to absorb energy from the fluid flow at the frequency of the predicted turbulent transition mode. Examples include textures and surface shapes configured to transfer energy of the fluid flow from the predicted turbulent transition mode to a different frequency.

Description

[Technical field]

[0001] [Government Rights] This invention was made with Government support under CMMI1727565 awarded by the National Science Foundation. The Government has certain rights in this invention.

[0002] CROSS-REFERENCE TO RELATED APPLICATIONS This application claims priority to and the benefit of U.S. Provisional Application No. 63 / 315,835, entitled "TURBULENCE SUPPRESSION METHODS AND DEVICES FOR PIPE AND CHANNEL FLOW," filed March 2, 2022, the contents of which are incorporated by reference in their entirety herein.

[0003] [Field] The following disclosure relates to methods and systems for actively and passively suppressing the transition of fluid flow from laminar to turbulent flow in a conduit, which is broadly defined as any confined or partially confined passage for transporting fluid, such as pipes of circular or other cross-sectional shapes, and channels, both open and closed. [Background technology]

[0004] The engineering of pipes and conduits for the transportation of liquids over long distances is a subject nearly as old as human civilization, with evidence dating back to antiquity through historical records of water routes, water clocks, and water organs. Some of the earliest known measurements of fluid flow properties through conduits date back to the construction of the water art gardens at Versailles during the late 17th century, and since then, steady progress has been made in refining the empirical observations and theoretical understanding of such flows.

[0005] It is now known that fluids can flow through conduits in two ways: laminar or turbulent. At low flow rates, the flow is laminar, characterized by an orderly velocity field aligned with the flow direction. As the flow rate increases, the flow suddenly becomes chaotic and complex, marking the transition to turbulence and turbulent flow. Turbulence and turbulent flow are then seen at all higher flow rates. Scientific efforts to model and understand this phenomenon began in earnest with Osborne Reynolds' pipe flow experiments in the 1880s, although closely related work had been accumulating since the last century. However, fully understanding the development of turbulent flow in pipes has remained elusive until today. This was dubbed the "turbulence problem" in 1921 and is one of the oldest unsolved problems in classical physics and remains an active area of ​​research.

[0006] Transition to turbulence in pipe flows is of great practical importance because it coincides with an abrupt increase in flow resistance through the pipe by a factor of about 10 compared to laminar flow, and the required pumping energy (and stress on the pump) also increases by the same factor. Finding ways to effectively control or delay transition to turbulence has been a "holy grail" in fluid engineering, alongside solving the turbulence problem in physics. However, technological progress has been small and incremental (e.g., minimizing pipe surface roughness, improving alignment of pipe segments, etc.). This lack of substantial progress is largely due to a limited real understanding of transition to turbulence, which is ultimately due to incomplete physical theories. In particular, the exact flow rate at which transition occurs can vary by orders of magnitude and is highly sensitive to many factors related to the pipe and its environment, including external disturbances, pipe geometry and surface finish, fluid properties, etc. While there is a wealth of intellectual property aimed at mitigating the onset of turbulence in duct flows, all known prior work is primarily derived from empirical observation and intuition, rather than insights rooted in a rigorous and thorough theoretical framework.

[0007] Today, in practice, almost all industrial-scale pipe flows operate well above the turbulent transition. The reasons for this operation are two-fold. First, laminar flow rates are often unrealistically slow. Second, flow rates near the transition can cause intermittent transitions between laminar and turbulent flow, which exert large cyclic stresses on the pipe walls, which significantly degrade the structural integrity of the pipe over time. This represents a cost trade-off between balancing the product delivery rate through the pipe against the costs for installation, energy consumption, and repairs. In virtually all industrial piping applications worldwide, the cost-optimal solution is to operate up to the turbulent regime. As a result, worldwide, pipe systems operate at approximately 10% less energy efficiency compared to laminar flow at the same flow rate, and collectively account for approximately 2% of the world's energy consumption. Summary of the Invention [Means for solving the problem]

[0008] This Summary is provided to introduce a selection of concepts that are further described below in the Detailed Description. This Summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used as an aid in limiting the scope of the claimed subject matter.

[0009] Certain aspects of the present disclosure provide a turbulence control system for a pipe or conduit comprising one or more modifications of the pipe or channel selected from the group including vibration inducing devices, textured surfaces, modified cross-sections or cross-sectional structures of pipe or channel liners, coatings and surface finishes, and conduit flexibility / deformation. In one embodiment, the one or more modifications of the pipe or channel are configured to suppress turbulent transition modes of the fluid or gas within the pipe or conduit.

[0010] Exemplary turbulence control systems of the present disclosure include vibration inducing devices attached to the inner or outer surface of a conduit or pipe, or within the wall thickness of a pipe or conduit, to perturb the fluid or gas within the pipe or channel. In some examples, a specific texture / pattern is placed on the inner surface of the pipe or channel. In some examples, the modifications change the flow-wise wavelength and / or cross-section of the pipe or channel such that the pipe or channel becomes disproportionate to the occurrence of transition modes. The modifications can include vibration absorbing materials lining the interior of the pipe or channel. In some examples, one or more coatings and / or surface finishes are applied to the interior of the pipe. Examples include conduit flexibility / deformation of the pipe channel, or materials therein, configured to absorb energy from turbulent transition modes.

[0011] In some examples, the turbulence control system includes an inspection gauge for the pipe or channel, where the pipeline inspection gauge is routed through the pipe or channel in a systematic manner for cleaning and inspection. In one embodiment, the inspection gauge is configured to travel through existing pipelines and retrofit them from the inside for turbulence suppression. The turbulence control system can include an inspection tool configured to travel inside or outside the pipe or channel for cleaning, inspection, and / or repair. In some examples, the inspection tool is configured to retrofit existing pipeline or channel lines for turbulence suppression. The turbulence control system can include manufacturing of new pipes or channels integrated with turbulence suppression technology. In some examples, the turbulence control system further includes construction site retrofits / retrofits of the pipe or channel for turbulence suppression.

[0012] One embodiment of the present disclosure is a system for controlling turbulence in a fluid flow in a conduit, the system including: a conduit configured to have a fluid flow therein; and at least one device associated with or integrated with the conduit and configured to generate disturbances in the fluid flow in the conduit to suppress calculated turbulent transition modes of the fluid flow. The turbulent transition modes may be calculated based on a turbulence model using a geometry of the conduit and one or more properties of the fluid, and further by calculating at least one response function and an excitation amplitude for each response function according to the turbulence model. In some embodiments, the turbulent transition modes are calculated according to Equation 12, and the generated disturbances are calculated as a function of Equation 4. In some embodiments, the conduit includes a pipe or a channel. The at least one device may be an inner surface of the conduit.

[0013] In some examples, at least the device includes an active flow perturbation device, and the system further includes a controller configured to instruct the active flow perturbation device, the active flow perturbation device configured to modify flow parameters of the fluid flow in the conduit in response to the controller, and the controller configured to generate the commands based on the calculated turbulent transition mode. The system can include at least one sensor configured to measure one or more characteristics of the fluid flow in the conduit associated with a transition between laminar flow and turbulent flow, and the controller further configured to generate the commands based on the measured characteristics. In some examples, the controller is configured to at least one of calculate or adjust the calculation of a turbulent transition mode or an amplitude response function of the turbulent transition mode of the fluid flow in the conduit based on the measured characteristics.

[0014] In some examples, the inner surface comprises a deformable material configured to absorb energy from calculated turbulent transition modes in the fluid flow, and the at least one device comprises a vibration inducing device positioned to introduce vibration energy into the fluid flow to suppress the calculated turbulent transition modes.

[0015] Another example of the present disclosure is a method of controlling a fluid flow in a conduit, the method including adjusting a flow of the fluid through the conduit to reduce turbulence therein based on the determined turbulence transition mode. The method can include determining the turbulence transition mode based on a turbulence model as a function of a geometry of the conduit and one or more properties of the fluid, and further by calculating at least one response function and an excitation amplitude for each response function according to the turbulence model. In some examples, the method includes calculating the turbulence according to Equation 12 and calculating an adjustment of the flow as a function of Equation 4.

[0016] In some examples, modulating the fluid flow includes selectively absorbing energy from the fluid at or near a calculated turbulent transition mode of the fluid flow. Modulating the fluid flow may include actuating an active flow control device configured to generate disturbances in the fluid flow in the conduit to suppress the calculated turbulent transition mode of the fluid flow. The method may include modulating the fluid flow with at least one device associated with or integrated with the conduit, where modulating the fluid flow includes introducing energy into or extracting energy from the fluid flow.

[0017] In some examples, the method includes sensing at least one characteristic of a fluid flow in a conduit associated with a transition between laminar flow and turbulent flow, and adjusting the fluid flow with at least one device based on the sensed at least one characteristic. The method can include calculating or adjusting a turbulent transition mode of the fluid flow in the conduit based on the sensed at least one characteristic, and adjusting the fluid flow with the at least one device is further based on the calculated or adjusted turbulent transition mode.

[0018] In some examples, the method includes modifying the conduit by altering a characteristic of an inner surface of the conduit or associating at least one device with the conduit, where the at least one device or the modified inner surface is configured to adjust fluid flow within the conduit to suppress a calculated turbulent transition mode of the fluid flow.

[0019] Yet another example of the present disclosure is a method of reducing turbulence in a fluid flow in a conduit, comprising: assuming fluid flow through the conduit, generating disturbances in the fluid flow in the conduit to suppress calculated turbulent transition modes of the fluid flow.

[0020] The following detailed description refers to the accompanying drawings, which form a part of this application and which show, by way of illustration, specific exemplary embodiments. Other embodiments may be made without departing from the scope of the disclosure.

[0021] The present disclosure will become more fully understood from the following detailed description taken in conjunction with the accompanying drawings, in which: [Brief description of the drawings]

[0022] [Figure 1] 1 is a graph of the turbulent kinetic energy spectrum E(k) versus wavenumber of turbulent fluctuations according to an embodiment of the presently disclosed theoretical model of fluid turbulence. [Diagram 2]FIG. 1 is a graph of the turbulent kinetic energy spectrum E(k) versus wavenumber of turbulent fluctuations for high-speed turbulent air flow through a circular pipe, where the data markers are past experimental measurements and the solid line represents the currently disclosed theoretical model of fluid turbulence. [Figure 3A] 1 is a graph of normalized flow perturbation velocity versus Reynolds number from a potential pilot experimental study of turbulent transition in a pipe flow. [Figure 3B] 3B is a graph of the prior experimental data of FIG. 3A rescaled according to the new turbulent transition model of the present disclosure. [Figure 4] FIG. 1 is a schematic cross-sectional view of a turbulence test apparatus according to an embodiment of the present disclosure. [Diagram 5] FIG. 1 is a perspective view of a pipe including an embodiment of an active turbulence control system of the present disclosure. [Figure 6] FIG. 1 is a transparent perspective view of a pipe having an embodiment of a passive turbulence control system of the present disclosure. [Figure 7] FIG. 1 is a perspective view of a pipe having an embodiment of a reactive turbulence control system of the present disclosure. [Figure 8A] FIG. 1 is a schematic perspective view of a conduit having a plurality of passive turbulence control structures disclosed on an inner surface of the conduit; [Figure 8B] 1 is a schematic front view of a conduit having a plurality of passive turbulence control structures disclosed on an inner surface of the conduit; [Figure 9] 1 is a schematic cross-sectional front view of a conduit having an exemplary active turbulence control system; [Figure 10] 1 is a schematic cross-sectional side view of a conduit having another exemplary conduit having an active turbulence control system; [Figure 11] FIG. 1 is a schematic side cross-sectional view of a conduit through which a remote device is moved that modifies the inner surface of the conduit to include an active turbulence control device and a fluid property sensor. [Figure 12] FIG. 1 is a perspective view of a pipe flow illustrating some of the key terminology and conventions used in turbulence modeling. [Figure 13] FIG. 1 is a perspective view of a channel flow illustrating some of the key terminology and conventions used in turbulence modeling. [Figure 14] FIG. 1 is a block diagram of an exemplary embodiment of a computer system for use with the present disclosure. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0023] Next, specific exemplary embodiments will be described to provide a general understanding of the principles of the structure, function, manufacture, and use of the devices and methods disclosed herein. One or more examples of these embodiments are illustrated in the accompanying drawings. Those skilled in the art will understand that the devices and methods specifically described herein and illustrated in the accompanying drawings are non-limiting exemplary embodiments, and the scope of the disclosure is defined only by the claims. Features illustrated or described in connection with one exemplary embodiment may be combined with features of other embodiments. Such modifications and variations are intended to be included within the scope of the disclosure. In this disclosure, similarly numbered and / or similarly named components of various embodiments generally have similar characteristics when those components are of similar nature and / or serve similar purposes, unless otherwise noted or understood otherwise by those skilled in the art.

[0024] The figures provided herein are not necessarily drawn to scale. Additionally, to the extent that arrows are used to describe directions of movement, these arrows are exemplary and do not limit the directions in which the respective components may or should be moved. Those of ordinary skill in the art will recognize, in light of this disclosure, other methods and directions for producing the desired results. Additionally, some terms may be used interchangeably throughout this disclosure, as would be understood by those of ordinary skill in the art.

[0025] To the extent the present disclosure includes various terms for components and / or processes of the disclosed devices, systems, aircraft, methods, etc., those of ordinary skill in the art will recognize in light of the claims, this disclosure, and the knowledge of one of ordinary skill in the art that such terms are merely examples of such components and / or processes and that other components, designs, processes, and / or actions are possible.

[0026] The articles "a" and "an" are used herein to refer to one or more than one (i.e., at least one) of the grammatical object of the article. By way of example, "an element" means at least one element and can include more than one element. "About" is used to provide flexibility to the endpoints of numerical ranges by allowing a given value to be "slightly above" or "slightly below" the endpoint without affecting the desired result. In this specification, the use of the terms "including," "comprising," or "having," and variations thereof, means to encompass the elements listed thereafter and their equivalents, as well as additional elements. As used herein, "and / or" refers to and encompasses all possible combinations of one or more of the associated listed items, as well as the absence of a combination when interpreted alternatively ("or"). Furthermore, the present disclosure also contemplates that in some embodiments, any feature or combination of features described herein may be excluded or omitted. By way of example, if a system or device is described herein as including components A, B, and C, it is specifically intended that either A, B, or C, or any combination thereof, alone or in any combination including, but not necessarily, other components (e.g., D, E, etc.), may be omitted and discarded.

[0027] The recitation of ranges of values ​​herein is intended to serve only as a shorthand method of individually referring to each individual value falling within the range, unless otherwise indicated herein, and each individual value is incorporated herein as if it were individually recited herein. For example, if a concentration range is recited as 1%-50%, values ​​such as 2%-40%, 10%-30%, or 1%-3%, are intended to be explicitly recited herein. These are merely examples of what is specifically intended, and all possible combinations of numerical values ​​between and including the lowest and highest values ​​recited are deemed to be explicitly recited in this disclosure. Unless otherwise defined, all technical terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure pertains.

[0028] Disclosed herein are systems and methods for suppressing laminar to turbulent transition of a fluid in a conduit, broadly defined as any bounded or partially bounded passage for fluid transport, such as pipes of circular or other cross-sectional shapes, and channels, both open and closed. Examples include active control systems that regulate flow characteristics, which may include both open and closed loop systems, as well as active systems that are implemented without inputs (such as systems with pre-determined logic or modeling that replace or supplement sensor inputs). Examples also include passive systems that are configured to selectively or preferentially respond to certain fluid flow characteristics and accordingly modify the fluid flow to reduce or suppress turbulent transitions (also referred to herein as turbulence onset or growth). Such passive and active systems can be stand-alone systems, but further examples include various combinations of active systems, passive systems, and active and passive systems together.

[0029] One aspect of the present disclosure is a physical system and method implementation of a theoretical model developed by the inventors and disclosed in further detail herein, which accurately predicts the critical set of parameters that transition laminar flow in a pipe to a self-sustaining turbulent state. These parameters broadly include fluid properties (e.g., density and viscosity), pipe geometry (e.g., cross-sectional shape, surface roughness, and alignment), and the environment in which the pipe is placed, specifically the spectrum of disturbances that may be imparted to the flow. The theoretical model presented herein reveals that for laminar flow there exists a subset of perturbation modes, specifically those called transitional modes, that are responsible for sustained turbulence when excited to sufficient amplitudes. The spectrum of disturbances in the flow, imposed by the external environment and excited by the flow itself, collectively excites the transitional modes, considering both the frequency-amplitude spectrum of the disturbances and the frequency-amplitude response functions of the transitional modes.

[0030] Examples disclosed herein include systems and methods configured to suppress excitation of transition modes, thereby allowing laminar flow to be maintained at relatively high flow rates. Specifically, in some examples, the transition mode response function can be primarily peaked near one particular frequency that is a function of flow parameters. This is referred to herein as the turbulent transition mode. Disturbances proportional to this frequency lead to resonant excitation, while most others are off-resonant. Examples of the present disclosure can only tolerate (or at least preferentially tolerate) off-resonant excitation of the fluid, which must be orders of magnitude larger in amplitude to cause sustained turbulence. Thus, examples of the present disclosure can effectively delay turbulent transition to higher flow rates. Additional context, details, and examples are provided herein. Below is a non-limiting and non-exhaustive list of exemplary turbulence suppression systems configured to reduce turbulent transition modes of fluid flow in a conduit. Examples include conduit modifications such as:

[0031] - Active flow perturbation devices, such as vibration inducing devices, that may be attached to the inner or outer surface of the conduit, or within the thickness of the conduit wall. These active devices are configured to perturb the fluid in a way that suppresses transition modes. Active perturbation devices may also include injection of fluids or gas bubbles, as well as magnetic manipulation of structures within the fluid flow.

[0032] - Passive flow perturbation devices, such as textured surfaces, including specific liners, finishes, or patterns on the interior conduit surface that directly interact with the fluid flow in the conduit and passively modify the fluid to suppress transition modes. Examples include textures or patterns that create specific flow structures that can transfer energy from turbulent transition modes. Examples of passive systems also include modified conduit cross sections that create regions of fluid flow with different turbulent transition modes. Because turbulent transition modes are three-dimensional, they can be suppressed by focusing on their flow direction wavelength, or cross-sectional structure. Examples include modifying the cross section of the conduit such that the geometry of the conduit is disproportionate to the occurrence of transition modes, thereby suppressing turbulence. Modification and design of the conduit geometry can be done based on calculations of predicted turbulent transition modes. The turbulent transition modes and their response functions are determined by the conduit geometry. Thus, for a given spectrum of disturbances imposed on the flow, examples include determining a conduit geometry (e.g., cross-sectional shape and / or flow direction path geometry) such that the amplitude response of transition modes does not meet the criteria for transitioning to turbulence for the given spectrum of disturbances. Examples include using artificial intelligence and / or machine learning (with or without more traditional computational optimization techniques) to design new conduit geometries and / or iterate conduit geometries towards a desired turbulent transition, flow rate, or other flow characteristics.

[0033] - A reactive flow absorbing device, such as a deformable liner or flexible conduit wall, configured to be acted upon by the flow and to absorb energy from the fluid flow, preferentially in the turbulent transition mode.

[0034] Exemplary implementation methods (and associated devices) include the fabrication of new pipes integrated with turbulence suppression technology utilizing embodiments disclosed herein, and retrofitting / retrofitting pipes at construction sites for turbulence suppression utilizing embodiments disclosed herein. The difference here is that there are more technical options to perform turbulence suppression on partially assembled pipes before construction is complete. Implementations can include retrofitting and using devices that are traditionally sent through pipelines periodically for cleaning and inspection, such as pipeline inspection gauges (PIGs) or pipeline inspection tools (PITs), configured to travel through existing pipelines and retrofit them from the inside for turbulence suppression. Examples of the present disclosure include such specialized devices. Of note, the turbulence suppression methods herein can be used to conversely induce turbulence in pipe flows. Thus, examples of the present disclosure can be generally considered turbulence suppression systems.

[0035] Examples of models disclosed herein correctly predict turbulent transition modes in pipes measured in various prospective experimental studies. The key insight is that a particular flow disturbance of wavelength λ0 (which is roughly twice the pipe diameter) is initially responsible for the laminar to turbulent transition of pipe fluid flow. Examples also include calculations of turbulent disturbance responses (e.g., turbulent transition modes) to fluid flow in conduits in general that are not strictly measured in diameter, but are nevertheless a function of one or more lengths characteristic of the geometry of the conduit. Any disturbance to a pipe flow (e.g., an obstacle, external vibration, and / or a bend in the pipe) can be analyzed in terms of the constituent wavelengths and corresponding amplitudes of the disturbances, particularly the degree to which each contributes to the excitation of λ0, where sufficient collective excitation of λ0 causes turbulence. Disturbance wavelengths similar to λ0 can cause resonant excitation, and very small amplitudes can cause the transition, while different wavelengths are off-resonance and require orders of magnitude larger amplitudes to cause the transition. As a result, the transition from laminar to turbulent flow in the conduit can be effectively delayed by suppressing disturbances on-resonance with λ, allowing the flow to become laminar and stabilize at a larger flow rate. Thus, embodiments of the present disclosure include systems and methods for actively and / or passively controlling transitional modes in a conduit flow to delay or prevent the transition from laminar to turbulent flow in the conduit fluid flow (e.g., increasing the flow rate required for the transition to occur), which control may include, for example, selective absorption or cancellation of transitional modes in the conduit flow fluid.

[0036] Examples of disturbance suppression can be implemented in a number of straightforward ways utilizing commercially available engineering hardware and software, which collectively constitute a set of technology options, as shown in further detail herein. Examples include retrofitting the exterior conduit walls with gentle vibration-inducing motors set to specific frequencies disproportionate to λ0 at specific locations, patterning the interior conduit walls with specific textures with periodicities disproportionate to λ0, and adding vibration damping materials specifically tuned with respect to λ0. Pressure and vibration sensors can also be implemented for monitoring or active control. These systems and methods can be applied to existing pipe infrastructure and to new pipe infrastructure at the point of construction with minimal logistical changes.

[0037] This disclosure includes an overview of a new fluid dynamics model of turbulence with a brief discussion of exemplary implementations, a more comprehensive description of the underlying mathematical model, and several non-limiting exemplary systems and methods that implement aspects of turbulent transition mode suppression based on this model.

[0038] The terms turbulent transition mode and calculated turbulent transition mode may refer to a single numerical value, but also encompass permutations of that numerical value, for example, as performed through one or more optimization techniques, modules, and the like. Additionally, while some aspects of the turbulent modes disclosed herein are presented for straight circular pipe flow, those skilled in the art will appreciate that other conduit geometries are possible, and that the mathematical framework presented herein is equally applicable to channel and conduit flows in general, with appropriate coordinates and constraints as would be known in the art. Nothing in this disclosure is intended to be limited in any manner to the specific circular pipe geometry used as an example for the derivation provided. Those skilled in the art will readily appreciate that any channel and conduit geometry can be used to develop specific turbulence models and subsequent turbulent transition modes for the flow conditions in that geometry, including using computational aids such as numerical modeling, to apply aspects of the present disclosure to complex geometries.

[0039] Further, embodiments of the present disclosure include using experiments to improve and / or tune the turbulent transition modes of a physical system. Because aspects of the turbulence models disclosed herein approximate certain flow characteristics (e.g., treating the flow as a continuum), an actual physical system may behave slightly differently. For example, the model of a pipe used herein assumes perfect symmetry and constant diameter, but such a perfect building is nearly impossible to achieve in practice, and similarly, fluid properties may vary slightly (e.g., changes in temperature or impurities). Thus, subtle deviations from the assumptions used in the turbulence models may result in small differences between the calculated turbulent transition modes and the response of the physical system. Embodiments of the present disclosure include using experiments to evaluate the ability of the calculated turbulent transition modes to reduce turbulence, and, if necessary, modifying or recalculating the calculated turbulent transition modes based on observations from the experiments. This may be performed using a controller of the system, whereby the calculated turbulent transition modes are used to modify the system, and measurements of the system are used to generate feedback to the controller to adjust the calculated turbulent transition modes used to modify the system. Examples include, given a calculated turbulent transition mode of a physical system, testing the physical system using the calculated turbulent transition mode to see if the measured system response matches the prediction, and if not, adjusting the implementation of the calculated turbulent transition mode based on the measurements. This may include, for example, recalculating the turbulent transition mode using new parameters / constraints that are experimentally determined to be a more accurate representation of the physical system. For example, a pipe may be assumed to be perfectly straight in a first calculated turbulent transition mode, and then testing may determine that the measured turbulent transition of the flow behaves more similarly to a pipe with a slight curve, asymmetry, or other deviation.A new turbulence model can then be generated to calculate new turbulent transition modes and / or a function can be determined to map the calculated turbulent transition modes to measurements of the physical system that is approximated by the turbulence model, thereby enabling the physical system to be controlled using the calculated turbulent transition modes and the experimentally determined mapping function.

[0040] New Fluid Dynamics of Turbulence From a theoretical point of view, an open challenge has been to develop a complete general mathematical framework that accurately captures the chaotic patterns of fluctuations observed in turbulent flows. The basic mathematical proposition of this problem is to find a general solution to the Navier-Stokes equations, the governing differential equations of motion for incompressible fluids, given by Equations 1A and 1B:

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[0041] The nonlinear convection term:

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[0042] Aspects of the present disclosure include a new general mathematical framework for turbulent fluids derived from first principles. In this context, the present disclosure includes a model framework that is the first general closed-form expression for the Navier-Stokes equations, which in itself constitutes an important theoretical advance for the general fluid dynamic description of physical systems. One insight centers around formalizing the turbulent fluctuation picture in a different way than Reynolds (i.e., Eqs. 2A and 2B) by decomposing the complete flow field v into a regular base flow U that exists in the absence of turbulent motion, plus a component u corresponding to all turbulent motion (e.g., v=U+u). One important difference is that the base flow U does not involve time averaging, corresponds to laminar flow through a domain of fluid, and is independent of additional fluid motions that may occur. This allows for an alternative modeling path that avoids the closure problem, where the turbulent motion is explicitly formulated in terms of U and represented through a closed-form velocity field u. In essence, the complete flow field is always considered to consist of at least a laminar portion U throughout the fluid domain v, which serves unambiguously as part of the domain definition of the turbulent motion u superimposed on it. From here, a spectral decomposition is performed on the turbulent part of the flow, which represents the complete dynamical picture in terms of turbulent kinetic energy density eigenstates. This new mathematical framework remedies for the first time several important theoretical challenges, two of which are highlighted below:

[0043] 1. Derivation of a complete turbulent energy spectrum from first principles. An example is shown in FIG. 1, which shows the turbulent kinetic energy E(k) as a function of wave number k of turbulent fluctuations in a turbulent fluid according to an embodiment of the presently disclosed theoretical model. The spectrum in FIG. 1 shows three typical regions of the energy spectrum: a generation range, which corresponds to fluctuations in the size of the fluid domain (and depends on the domain's shape); an intermediate range (often called the inertial subrange), which corresponds to an inviscid cascade of energy from small to large wave numbers; and a dissipation range, where viscous dissipation is significant. Detailed experimental measurements of turbulent energy spectra have been reported over the past 60 years, but no part of the energy spectrum has been mathematically rigorously derived. Comparison of examples of the presently disclosed model with published experimental data provides excellent agreement and helps validate the present turbulence model. FIG. 2 shows historical data measuring the turbulent energy spectrum of highly turbulent air flowing through a circular pipe, overlaid with curves corresponding to embodiments of the presently disclosed theoretical model.

[0044] 2. Predicting laminar-turbulent transition in pipe flows. Predicting the transition from laminar to turbulent flow in cylindrical pipes is considered a classical unsolved theoretical problem, first posed as a scientific problem by Reynolds in the 1880s. Using the theoretical turbulence model described herein, the critical flow parameters that define the turbulent transition in cylindrical pipes can be derived, and the prospective experimental data published in the past 30 years can be successfully collapsed onto a single curve, further confirming the existence of a universal power law. A representative example of the prior experimental data is shown in FIG. 3A (described in more detail below), and the collapse of this data according to an example of the theoretical turbulence model is shown in FIG. 3B. Certain aspects of the present disclosure exploit insights related to these results, which in some examples are translated into specific systems and methods for suppressing or reducing the occurrence of turbulence in pipes and conduits.

[0045] Before detailing specific insights, implications, and exemplary embodiments arising from the presently disclosed turbulence model, prior experimental work in the academic literature is described that measures the transition from laminar to turbulent flow in a straight circular pipe of diameter D=2R, where R is the radius of the pipe. FIG. 4 illustrates a standard experimental procedure 100 for introducing a precise disturbance to a fully developed, time-independent laminar flow through a pipe. The exemplary system 100 includes a fluid source 101 and a conduit 110 through which a laminar flow 102 of fluid is generated (direction of fluid flow as indicated by arrow 109). The system 100 includes an inlet 120 to the conduit 110 where disturbances to the laminar flow 102 may occur, and a region 130 downstream from the inlet 120 where flow conditions may be observed. Flow can be observed many pipe diameters downstream, where the first instances of distinct, persistent turbulent "puffs" mark the transition boundary between relaminarizing and persistent disturbances. In practice, for pipe flows, turbulent puffs are consistently observed experimentally to be in the range of about 5 to about 10 pipe diameters in length, surrounded by laminar flow upstream and downstream, and flowing at approximately the average velocity of the flow.

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[0046] The data in Figures 3A and 3B include experimental measurements from three different papers (described in more detail below), with the different data point shapes indicating the corresponding paper and the different shaded fills indicating each separate experimental run. A brief description of the flow perturbation methods in each paper in Figures 3A and 3B is provided below.

[0047] The solid data points in Figures 3A and 3B show experimental results from a 2003 paper by Hof et al. (Scaling of the turbulence transition threshold in a pipe, Physical Review Letters, 91:244506, 2003). In these experiments, a square pulse of fluid injection was introduced through six small holes in the inner pipe wall. The metric of disturbance was the streamwise length of the disturbed flow.

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[0048] The first (downward) shaded data points in Figures 3A and 3B show experimental results from a 2005 paper by Hof (Transition to turbulence in pipe flow. Fluid Mechanics and its Applications, 77, 2005). In these experiments, the flow was perturbed in a manner similar to the 2003 Hof results in Figures 3A and 3B, but the fluid pulse was delivered through one relatively large hole in the inner pipe wall instead of six.

[0049] The second (downward) shaded data points in Figures 3A and 3B show experimental results from a 2008 paper by Nishi et al. (Laminar-to-turbulent transition of pipe flows through puffs and slugs. Journal of Fluid Mechanics, 614). In these experiments, a ring-shaped obstacle was placed in the pipe to perturb the flow. The ring featured an outer radius identical to the inner radius of the pipe, and an inner radius of smaller diameter. The metric of the amplitude perturbation was the radial thickness of the ring (i.e., the difference between the outer and inner radii of the ring). The pipe flow rate was increased in steps until the turbulent transition was reached.

[0050] An important observation from these previous studies on transition to turbulence is the different trends in transition exhibited by each experimental run. This is evident in Figure 3A, where the horizontal axis is the non-dimensional flow rate through the pipe.

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[0051] According to the theoretical model presented here, the specific wavelength of the disturbance in the flow, λ, that is responsible for the laminar-turbulent transition is i These wavelengths can be identified in order of decreasing size (i.e., {λ0, λ1, λ2, ...}), which represents an ordered list of wavelengths of decreasing size. Equivalently, these fluctuations are expressed by the wavenumber k i ≡2π / λ ican be thought of in terms of a corresponding ordered list of increasing wavenumbers {k0,k1,k2,...}. Any disturbance to the fluid flow in the pipe (e.g., an obstacle, external vibration, bends in the pipe, surface roughness, etc.) will have its constituent wavelengths and corresponding amplitudes, in particular, each of these specific wavenumbers k i can be analyzed in terms of the degree to which it contributes to exciting k i The velocity amplitude of the disturbance corresponding to k and has an amplitude u k When i is large enough, persistent turbulence is induced.

[0052] The significance of ordering the specific set of wave numbers responsible for laminar-turbulent transition as {k0,k1,k2,...} is as follows. These specific spatial variations in turn become important for turbulent transition as the dimensionless flow rate Re increases. For example, when Re is small, only k0 is important for determining the transition criterion. As Re increases, it turns out that the set {k0,k1} becomes important. As Re increases further, it may be necessary to consider the set {k0,k1,k2}, etc.

[0053] The physical picture of laminar-turbulent transition explained earlier is i Response function R i (k), and this response function R i (k) is the spectrum of velocity fluctuations present in the fluid, u δ (k) and this product is integrated over all k. If the wave number is non-dimensionalized by the pipe radius κ ≡ Rk, the integral formula becomes:

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[0054] Exemplary Turbulence Control System Examples of the present disclosure also include systems and methods for controlling turbulence in a conduit flow based on turbulent transition modes calculated using the turbulent transition models disclosed herein. Examples may include calculating one or more turbulent transition modes for a given conduit or conduit flow, and modifying the fluid flow in the conduit to suppress the turbulent transition modes. Examples include configuring a device and / or modifying the conduit to generate disturbances in the fluid flow that suppress the turbulent transition modes, and other examples include devices and methods that selectively / preferentially absorb energy from the turbulent transition modes in the fluid flow, thereby suppressing the turbulent transition modes. Examples also include systems that measure, sense, or otherwise observe the fluid flow in the conduit (optionally including measuring any other parameters relevant to the calculation of the turbulent transition modes, including geometric parameters of the conduit), and calculate the turbulent transition modes to control the generation of disturbances in the fluid flow and suppress the turbulent transition modes, which may be performed offline, remotely, and / or in real time. These and other embodiments can be implemented in numerous ways utilizing commercially available engineering hardware and software, which collectively constitute a set of technology options, specific examples of which are illustrated in Figures 5-11. In general, embodiments include calculating turbulent transition modes for a given conduit flow, which may be for a particular flow condition, or for multiple possible flow conditions through the conduit, and using the presently disclosed turbulence models to reduce turbulence in the conduit flow by causing suppression of the calculated turbulent transition modes in the fluid flow within the conduit.

[0055] According to the presently disclosed turbulence model, suppression of the calculated turbulent transition modes in the conduit fluid flow delays or prevents the transition from laminar fluid flow to a turbulent state in the conduit. This allows, for example, higher laminar fluid flow rates to be achieved in the conduit as long as the suppression of the turbulent transition modes is sustained. Additionally, in dynamic flow conditions, examples include active open-loop and closed-loop control, which may include, for example, sensors or other measurement techniques to generate information regarding the state of the fluid flow in the conduit and then (including in real-time) use a control system to generate / adjust flow disturbance commands provided to active flow disturbance devices (in fluid communication) that maintain the suppression of the turbulent transition modes. Examples of active control may be used when flow conditions change, for example, due to the initiation of fluid flow or some change in the fluid flow, for example, due to temperature changes, flow rate changes, pressure changes, or any other fluid parameter that may affect the turbulent transition modes. Examples include real-time calculation of turbulent transition modes, which may be used, for example, when conduit parameters and / or flow parameters change. Conduit parameters may change, for example, due to temperature changes in the fluid causing thermal contraction / expansion of the conduit structure, which may change the conduit geometry and thereby the turbulent transition mode.

[0056] Examples also include using feedback directly from the flow perturbation device, such as back pressure (in the case of fluid ejection devices) or impedance (in the case of electrical devices such as vibration inducing devices). In these examples, the ability to drive the perturbation device may be used by the control system to determine the state of the fluid being perturbed and therefore whether turbulent transition modes are being suppressed as desired. Additionally, one skilled in the art will appreciate that numerous techniques exist for sensing conduit flow conditions, including parameters particularly related to laminar and turbulent flow, and any of these existing techniques may be combined with a control system including one or more active flow control devices within the conduit (or otherwise mechanically, thermally, acoustically, magnetically, electromagnetically, and / or fluidically coupled to the fluid flow within the conduit) that may be used to suppress turbulent transition modes of the fluid flow within the conduit. Examples also include using input from fluid conditions upstream and / or downstream of the conduit, which may be used to extrapolate flow parameters within the conduit. Examples also include movable flow control structures, such as articulating surfaces or vanes, that may be positioned within the conduit or that are positionable from a position outside the conduit (and / or outside the fluid flow) to an insertion or deployment position in the flow. In the fluid flow, the geometric and positional parameters of the structures (e.g., extension, penetration, angle of attack, etc.) can be adjusted by a control system to modify the flow parameters of the fluid flow to suppress turbulent flow control modes. Additional non-limiting examples include control structures that are movable parts of the conduit wall.

[0057] Examples of the present disclosure also include passive and reactive turbulence control systems configured to absorb and / or suppress calculated turbulent transition modes of the fluid flow in the conduit, with or without active control. Here, the term reactive refers to structures that move or otherwise react to the fluid flow in a particular manner to absorb energy from the fluid to suppress turbulent transition modes of the fluid, and the term passive refers to static structures, coatings, and textures that are not configured to utilize kinetic energy from the fluid flow to modify the fluid flow to suppress turbulent transition modes of the fluid. Examples include liners, such as flexible or deformable liners, disposed on at least a portion of the inner wall of the conduit and configured to absorb energy from turbulent transition modes of the fluid flow. An exemplary line can have material properties that preferentially deform at or near the turbulent transition modes such that energy from the fluid at or near the turbulent transition modes is transferred to deformation of the liner, thereby suppressing the turbulent transition modes of the fluid. Examples include patterns, textures, and / or coatings on the inner walls of a conduit that modify fluid properties as the flow flows across the pattern, texture, and / or coating, the modified fluid properties causing suppression of turbulent transition modes of the fluid. Examples of passive control include movable structures / surfaces that are not actively controlled but otherwise move or can move in the fluid flow in response to the movement of the fluid such that the structure / surface absorbs energy from turbulent transition modes in the fluid.

[0058] 5-11 show exemplary embodiments for turbulence control. FIG. 5 shows an exemplary turbulence control system 500 including a conduit 501 with vibration inducing devices 511 placed at strategic locations on the outside of the conduit 501, which can optionally include sensors 512 for closed loop control. FIG. 6 shows an exemplary turbulence control system 600 including a patterned texture 621 on the inside surface of the conduit 601. FIG. 7 shows an exemplary turbulence control system 700 including a conduit 701 with a specially tailored vibration damping material 731 lining the inside of the conduit 701. For any of the examples presented herein, the inner walls of the conduit (e.g., the walls in contact with the fluid flowing through the conduit) may be coated to ensure chemical compatibility. Additionally or alternatively, vibration damping materials may be introduced between the pipe and its external support structure.

[0059] Exemplary systems and implementations of turbulence control enabled by aspects of the present disclosure may be implemented to control κ at specific locations and / or associated (e.g., as the active turbulence control system of FIG. 5 ). i Examples include retrofitting the external pipe wall with gentle vibration-inducing motors set to a specific frequency that is mismatched with the associated κ (e.g., using the passive turbulence control system of FIG. 6). i Patterning the internal pipe wall with a specific texture that has a periodicity disproportionate to κ and controlling the associated κ (e.g., using the reactive turbulence control system of FIG. 7) i Examples also include adding vibration damping materials specifically tailored for the pressure and vibration sensors implemented for monitoring or active control. These methods can be applied to existing pipe and conduit infrastructure, and to new pipe and conduit infrastructure at the point of construction with minimal logistical changes.

[0060] An exemplary system 500 including a conduit 501 (e.g., a pipe as shown) and an active turbulence control system according to an embodiment of the disclosure is shown in FIG. 5. The active turbulence control system includes a controller 519, a vibration inducing device 511 disposed on an exterior portion of the conduit 501, and a sensor 512 configured to sense a parameter indicative of a condition of the fluid flow within the conduit 501. Although FIG. 5 shows a single vibration inducing device 511 and a single sensor 512, this is merely by way of example and embodiments include multiple devices and / or sensors that can operate together or individually. The vibration inducing device 511 can be configured to create flow disturbances in the fluid flowing through the passage 502 of the conduit. The flow disturbances generated by the vibration inducing device 511 can be specifically configured to suppress certain frequencies of energy in the fluid flow within the passage 502 of the conduit 501, where the suppressed frequencies are based on or near a calculated turbulent transition mode of the flow within the passage 502. The turbulent transition mode may be calculated according to any aspect of the presently disclosed turbulence control model. The controller 519 may calculate or adjust the calculation of the turbulent transition mode based on information received from the vibration inducing device 511 and / or the sensor 512, as the case may be. The controller 519 may be external to the conduit and / or may be incorporated as part of one or more of the devices 511 / sensors 512. In other words, the controller may be located virtually anywhere, even though it is illustrated as being "outside" the conduit. The sensor 512 may be located within the conduit 501, on or around an outer portion of the conduit (as shown), or otherwise associated with the conduit 501, and measurements or observations of information indicative of fluid flow within the conduit may be received and provided to the controller 519, for use in, for example, adjusting the generated flow disturbances and / or adjusting the calculated turbulent transition mode. During operation, fluid flowing through the passageway 502 of the conduit 501 can be acted upon by the vibration inducing device 511, thereby, for example, achieving high flow rates without transitioning the fluid flow into turbulence.The controller 519 can be used, for example, to suppress turbulence at a number of different flow conditions and even for different fluids and fluid properties.

[0061] Alternatively, the vibration inducing device 511 can act on the fluid flow to increase the energy of the fluid flow in a turbulent transition mode and reduce the fluid flow rate at which the fluid flow transitions to turbulence. The vibration inducing device 511 can be added to an existing conduit and / or integrated into or associated with a new conduit during or after the manufacture of the conduit. While the vibration inducing device 511 in FIG. 5 is shown as being external to the passageway 502, examples include devices having both external and internal components, such as a vibration inducing device having a motor external to the conduit and an emitter coupled to the external motor that extends through an opening in the conduit 501 and into the passageway 502, among other configurations for a vibration inducing device that one of skill in the art may use with a conduit having the nature of the conduit 501 in light of this disclosure without departing from the spirit of the disclosure.

[0062] An exemplary system 600 including a conduit 601 (e.g., a pipe as shown) and a passive turbulence control system according to an embodiment of the present disclosure is shown in FIG. 6. The passive turbulence control system includes a plurality of flow disturbance inducing features 621 disposed on an inner wall of the conduit 601. The flow disturbance inducing features 621 may be configured to create flow disturbances in a fluid flowing through a passage 602 of the conduit 601. The flow disturbances generated by the flow disturbance inducing features 621 may be specifically configured to suppress certain frequencies of energy in the fluid flow within the passage 602 of the conduit 601, the suppressed frequencies being on or near a calculated turbulence transition mode of the fluid flow within the passage 602. The turbulence transition mode may be calculated according to any embodiment of the presently disclosed turbulence control model. The flow disturbance inducing features 621 may include, for example, patterns, textures, raised or reduced areas and surfaces, and coatings and / or finishes on the inner wall of the conduit 601.

[0063] An exemplary system 700 including a conduit 701 (e.g., a pipe as shown) and a reactive turbulence control system according to aspects of the disclosure is shown in FIG. 7. The reactive turbulence control system includes an elastically deformable liner 731 disposed on or forming an inner wall of the conduit 701. The elastically deformable liner 731 is configured to create flow disturbances in the fluid flowing through a passageway 702 of the conduit 701 by absorbing energy from the fluid. The flow disturbances created by the elastically deformable liner 731 may be specifically configured to suppress certain frequencies of energy in the fluid flow within the passageway 702 of the conduit 701, the suppressed frequencies being on or near a calculated turbulent transition mode of the fluid flow within the passageway 702. The turbulent transition mode may be calculated according to any aspect of the presently disclosed turbulence control model. The elastically deformable liner 731 may be constructed from one or more materials, including internal and external structures, voids, and / or other inhomogeneities, to create specific responses by the elastically deformable liner 731 to specific flow conditions, such as oscillations of the fluid at or near the turbulent transition mode. During operation, the elastically deformable liner 731 may preferentially respond to motions in the fluid at or near the turbulent transition mode, which motions cause peaks in the elastically deformable liner 731 motion, thereby transferring energy from the fluid to or near the turbulent transition mode. Exemplary elastically deformable liners may also include features of the passive turbulence control system disclosed herein, such as patterns or surface textures or coatings. Additionally, the elastic deformable liner may include an active control system that can, for example, modify the elasticity or other properties of the liner by, for example, changing the fluid pressure in cavities within the elastic deformable liner, and / or moving additional fluid into or out of the elastic deformable liner, and / or activating mechanical systems therein, such as shock absorbers, dampers, and / or smart materials with tunable mechanical response properties.

[0064] Another exemplary system 800 including a conduit 801 (e.g., a square channel as shown) and a passive turbulence control system according to aspects of the present disclosure is shown in FIGS. 8A and 8B. The passive turbulence control system includes a plurality of flow disturbance inducing features 821 disposed on an inner wall of the conduit 801. The flow disturbance inducing features 821 are configured to generate flow disturbances in a fluid flowing through a passageway 802 of the conduit 801. The flow disturbances generated by the flow disturbance inducing features 821 may be specifically configured to suppress certain frequencies of energy in the fluid flow within the passageway 802 of the conduit 801, where the suppressed frequencies are on or near a calculated turbulent transition mode of the fluid flow within the passageway 802. The turbulent transition mode may be calculated according to any aspect of the presently disclosed turbulence control model. The low disturbance inducing features 821 in Figures 8A and 8B are protrusions that extend inwardly into the passageway 802 and can, for example, vary the turbulent transition mode across the width of the passageway 802, such that, for example, there are multiple turbulent transition modes. This can induce a transfer of energy between adjacent regions of the passageway 802, moving energy away from the calculated dominant turbulent transition mode of the passageway 802, thereby increasing the flow rate through the conduit 801 before turbulent transition occurs. Figures 8A and 8B show the disturbance inducing features 821 as alternating around the lateral periphery, but the flow direction and any other direction are possible and can depend, for example, on the flow disturbance required to suppress the dominant turbulent transition mode of the conduit 801.

[0065] Another exemplary system 900 including a conduit 901 (e.g., a pipe as shown) and an active turbulence control system according to an embodiment of the disclosure is shown in FIG. 9. The active turbulence control system includes a controller 990, a plurality of movable flow control devices 911 disposed in and extending from an interior portion of the conduit 901, and a plurality of sensors 912 configured to sense parameters indicative of fluid flow conditions within the conduit 901. The movable flow control devices may be configured to create flow disturbances in the fluid flowing through the passage 902 of the conduit 901, which may be done, for example, by moving or positioning the movable flow control devices 911, which may include, for example, vanes or other flow control surfaces and structures known in the art. The system includes a motor 913 coupled to the movable flow control devices 911 to control their movement and / or position. The flow disturbances generated by the movable flow control device 911 may be specifically configured to suppress certain frequencies of energy in the fluid flow within the passage 902 of the conduit 901, the suppressed frequencies being on or near a calculated turbulent transition mode of the flow within the passage 902. The turbulent transition mode may be calculated according to any aspect of the presently disclosed turbulence control model. The controller 990 may, in some cases, calculate or adjust the calculation of the turbulent transition mode based on information received from the motor 913 and / or the sensor 940. The sensor 940 may be located within the conduit 902 (as shown), on or about an outer portion of the conduit, and / or otherwise associated with the conduit 901, and measurements or observations of information indicative of the fluid flow within the conduit may be received and provided to the controller 990 for use, for example, in adjusting the generated flow disturbances and / or adjusting the calculated turbulent transition mode. During operation, fluid flowing through passageway 902 of conduit 901 can be acted upon by movable flow control device 911, thereby, for example, achieving high flow rates without transitioning the fluid flow into turbulence.

[0066] Yet another exemplary system 1000 including a conduit 1001 and an active turbulence control system according to an embodiment of the disclosure is shown in FIG. The active turbulence control system includes a controller 1090, a plurality of flow control devices 1011 configured to adjust the position and shape of an inner portion 1009 of the conduit 1001, and a plurality of sensors 1012 configured to sense parameters indicative of a condition of fluid flow within the conduit 1001. The flow control devices 1011 may be configured to create flow disturbances in the fluid flowing through the passageway 1002 of the conduit 1001 (as indicated by arrows 1099) by controlling the position and shape of the inner portion 1009. The system 1000 includes a motor 1013 coupled to each flow control device 1011 to control their movement and / or position, thereby controlling the position and shape of the inner portion 1009. The flow disturbances generated by the movable inner portion 1009 may be specifically configured to suppress certain frequencies of energy in the fluid flow within the passage 1002 of the conduit 1001, the suppressed frequencies being on or near a calculated turbulent transition mode of the flow within the passage 1002. The turbulent transition mode may be calculated according to any aspect of the presently disclosed turbulence control model. The controller 1090 may calculate or adjust the calculation of the turbulent transition mode based on information received from the motor 1013 or the sensor 1012, as the case may be. The sensor 1012 may be located within the conduit 1002 (as shown), on or about an outer portion of the conduit, or may be otherwise associated with the conduit 1001, and measurements or observations of information indicative of the fluid flow within the conduit may be received and provided to the controller 1090, for use in, for example, adjusting the generated flow disturbances and / or adjusting the calculated turbulent transition mode. During operation, fluid flowing through passageway 1002 of conduit 1001 may be acted upon by inner portion 1009, thereby, for example, achieving high flow rates without transitioning the fluid flow to turbulent flow.

[0067] Another embodiment of the present disclosure is a system for modifying a conduit to include any of the flow control devices, structures, etc. disclosed herein. Figure 11 is a schematic side cross-sectional view of a conduit 1101 with a remote device 1180 moving within a passageway 1102 of the conduit 1101 (as indicated by arrow 1199) that has modified the inner surface of the conduit 1101 to include an active turbulence control device 1111 and a fluid property sensor 1112, either of which may be configured to communicate with a controller 1190 that may be located near the conduit 1101 or elsewhere. Additionally, any and all of the previous teachings and understandings related to other embodiments presented herein are applicable to this embodiment.

[0068] Detailed physical picture of turbulent transition In this section, we detail the physical picture for the laminar to turbulent transition of fluid flow through a straight circular pipe of diameter D = 2R, as shown in Figure 12. This transition has been experimentally measured in the literature, with results obtained by introducing a precise disturbance into a fully developed, time-independent laminar flow. The flow is then observed several pipe diameters downstream, where the first instances of distinct turbulent "puffs" indicate the transition boundary between the relaminarizing and persistent disturbances. The turbulent puffs have been experimentally observed to be approximately 5-10 pipe diameters long, are surrounded by laminar flow upstream and downstream, and flow at approximately the mean velocity of the flow.

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[0069] Laminar flow through a pipe is

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[0070] Mechanism of turbulence generation We now explain the mechanism of generation of the self-sustaining turbulent puffs utilized in the turbulence model disclosed herein. If a portion of a laminar flow is displaced in any radial direction, e.g. radially inward, the streamwise velocity of the displaced fluid particles can be smaller than the local background flow due to the velocity gradient as defined by Equation 1 above. The radial component of the flow disturbance is special in this respect. It is because

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[0071] Due to the cylindrical geometry of the pipe, low-speed streaks near the center of the pipe are closer to each other than high-speed streaks near the circumference of the pipe. This allows adjacent low-speed streaks to merge, which may help reduce the overall viscous dissipation of the disturbed flow field. The simplest case is a pairwise merger, where one would expect to see n low-speed streaks near the center of the pipe and 2n high-speed streaks near the circumference of the pipe, where n is the integer number determined by the Reynolds number

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[0072] However, counter-rotating vortices themselves are unstable and can give rise to instabilities with respect to the cross-section of the vortex core (e.g., elliptical instability) as well as the streamwise path of the vortex core (e.g., crow instability); these instabilities arep ~d c and λ p ~5-10d c Each wavelength is about d c is the diameter of the vortex core. Both of these wavelengths are believed to exist experimentally, the latter affecting the length of the turbulent puff. Here, the path wavelength λ p develop in phase for each counter-rotating pair of vortices and can grow in amplitude until the vortex cores cross, resulting in the streamwise vortex cores being sandwiched into vortex rings. These vortex rings have a streamwise length λ p and serves to divide the disturbed flow field into discrete segments. c is a fraction of the pipe radius R, so λ p ~a few R.

[0073] It can be important to keep in mind that the vortex structures described above are only observed through near-instantaneous experimental measurements of the disturbed flow field. At longer times, the flow appears highly chaotic and the length scales of the series of turbulent eddies are

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[0074] The energy to sustain the puff can be provided by the laminar background flow. As a simple magnitude estimate, we can compare the laminar flow field with a time-averaged turbulent flow that is approximately uniform over the cross section of the pipe. This gives the relative change in the velocity field:

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[0075] Equation 10 represents the energy available to "put into" the puff at the upstream boundary. A persistent turbulent puff balances this energy input with its viscous dissipation. For small Re (Reynolds number), viscous dissipation dominates and the puff eventually relaminarizes. For larger Reynolds numbers, the puff grows in length and may even split into two, both of which acquire a persistent configuration separated by an interlaminar region.

[0076] This behavior can be rationalized in light of the mathematical scheme above.

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[0077] The steady-state minimum length of the interlaminar region between puffs is determined by the degree of laminar development required at the boundary with the downstream puff for self-sustaining. It is easy to see that this length can be smaller for larger Re. Conversely, decreasing Re from within the turbulent state space approaches a transition boundary for a puff to sustain, where the laminar profile must approach the limit of full development (see Eq. 7), and thus is formally of infinite length. This is consistent with experimental observations, where at transition boundaries, turbulent puffs first appear rare and are separated by arbitrarily large distances. As Re increases, puffs appear more frequently and more closely spaced. When close together, puffs interact with each other in complex ways, splitting and merging until eventually the entire flow is uniformly turbulent.

[0078] scaling Considering the previous section, the neutrally stable mode that indicates turbulent transition corresponds to a balance between the viscous and nonlinear terms in the Navier-Stokes equations (Eq. 1a), which is related to the scaling

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[0079] Equations 11 and 12 together define the transition boundary. In other words, Equation 12 represents the threshold at which the kinetic energy supplied to the puff from the laminar base flow is sufficient to balance the viscous dissipation of the puff, while the disturbance amplitude initially required to induce turbulence is given by Equation 11. For Equation 11, the two sides of

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[0080] In general, the turbulent regime involves a series of length scales spanning many orders of magnitude, from which a near infinite number of quasi-modes can be constructed. However, the situation at the transition boundary is rather simplified. It is natural to assume that the quasi-mode with the longest wavelength (e.g., the smallest wave vector) is the main cause of the transition. This particular one experiences the smallest viscous dissipation and therefore persists for the longest time with finite amplitude, during which energy can be transferred to eigenstates allowed by the particular selection rule resulting from the nonlinear term in Eq. 1A. The wavelength of this quasi-mode is fixed by the geometry of the pipe, regardless of Re. Since the nonlinear term is quadratic (see Eq. 1A), the energy exchange occurs mainly between wavelengths that differ by a factor of two, taking into account the azimuthal and axial symmetries of the pipe. Moreover, the nonlinear term mixes vector components in all coordinate directions, which means that the wavelengths allowed by the selection rule are balanced for both the cross-section of the pipe and the flow direction. The longest wavelengths that satisfy this condition are λ = 2R, 4R, corresponding to the cross-section and flow direction, respectively. Thus, the wave vector

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[0081] External disturbance spectrum u mediated by energy transfer through quasi-modes δ Eigenstate u by (κ) αThe net excitation amplitude of is given by Equation 4, shown above and presented again here:

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[0082] The systems and methods described herein can be implemented in hardware, software, firmware, or a combination of hardware, software, and / or firmware. In some embodiments, the systems and methods described herein can be implemented using a non-transitory computer-readable medium that stores computer-executable instructions that, when executed by one or more processors of a computer, cause the computer to perform operations. Computer-readable media suitable for implementing the systems and methods described herein include non-transitory computer-readable media such as disk memory devices, chip memory devices, programmable logic devices, random access memories (RAMs), read-only memories (ROMs), optical read / write memories, cache memories, magnetic read / write memories, flash memories, and application-specific integrated circuits. Furthermore, the computer-readable media implementing the systems or methods described herein may be located on a single device or computing platform, or may be distributed across multiple devices or computing platforms.

[0083] FIG. 14 provides one non-limiting example of a computer system 1400 on which the present disclosure can be constructed, executed, trained, etc. For example, referring to FIG. 5, FIG. 9, FIG. 10, and FIG. 11, processing modules or processors 590, 990, 1090, 1190 may be examples of the system 1400 described herein. The system 1400 may include a processor 1410, a memory 1420, a storage device 1430, and an input / output device 1440. Each of the components 1410, 1420, 1430, and 1440 may be interconnected, for example, using a system bus 1450. The processor 1410 may process instructions executed within the system 1400. The processor 1410 may be a single-threaded processor, a multi-threaded processor, or a similar device. The processor 1410 may be capable of processing instructions stored in the memory 1420 or on the storage device 1430. The processor 1410 may perform operations such as calculating turbulent transition modes, calculating flow disturbances to suppress turbulent transition modes, or adjusting predicted turbulent transition modes based on information received from one or more sensors that measure the fluid flow, among other features described in connection with this disclosure, including any control logic associated with the operation of an active turbulence suppression system or device.

[0084] The memory 1420 can store information within the system 1400. In some implementations, the memory 1420 can be a computer-readable medium. The memory 1420 can be, for example, a volatile or non-volatile memory unit. In some implementations, the memory 1420 can store, among other information, conduit geometry, fluid flow parameters (predicted or measured), information related to turbulent transition modes, any information related to the calculation of turbulent transition modes.

[0085] The storage device 1430 can provide mass storage to the system 1400. In some implementations, the storage device 1430 can be a non-transitory computer-readable medium. The storage device 1430 can include, for example, a hard disk device, an optical disk device, a solid-date drive, a flash drive, a magnetic tape, or some other mass storage device. The storage device 1430 can alternatively be a cloud storage device, for example, a logical storage device including multiple physical storage devices distributed over a network and accessed using the network. In some implementations, information stored on the memory 1420 can also or instead be stored in the storage device 1430.

[0086] The input / output devices 1440 can provide input / output operations to the system 1400. In some implementations, the input / output devices 1440 can include one or more of a network interface device (e.g., an Ethernet card), a serial communication device (e.g., an RS-232 10 port), and / or a wireless interface device (e.g., a short-range wireless communication device, an 802.11 card, a 3G wireless modem, or a 4G wireless modem). In some implementations, the input / output devices 1440 can include driver devices configured to receive input data and send output data to other input / output devices, such as keyboards, printers, and display devices. In some implementations, mobile computing devices, mobile communication devices, and other devices can be used.

[0087] In some implementations, system 1400 may be a microcontroller. A microcontroller is a device that includes multiple elements of a computer system in a single electronics package. For example, the single electronics package may include a processor 1410, a memory 1420, a storage device 1430, and an input / output device 1440.

[0088] Although an exemplary processing system has been described above, embodiments of the subject matter and the functional operations described above may be implemented in other types of digital electronic circuitry, or computer software, firmware, and / or hardware, including the structures disclosed herein and their structural equivalents, or a combination of one or more of them. Embodiments of the subject matter described herein may be implemented as one or more computer program products, i.e., one or more modules of computer program instructions encoded on a tangible program carrier, such as a computer-readable medium, for execution by or to control the operation of a processing system. The computer-readable medium may be a machine-readable storage device, a machine-readable storage substrate, a memory device, a composition affecting a machine-readable propagated signal, or a combination of one or more of them.

[0089] Various embodiments of the present disclosure may be implemented, at least in part, in any conventional computer programming language. For example, some embodiments may be implemented in a procedural programming language (e.g., "C"), or an object-oriented programming language (e.g., "C++"). Other embodiments of the present invention may be implemented as pre-configured, stand-alone hardware elements and / or pre-programmed hardware elements (e.g., application specific integrated circuits, FPGAs, and digital signal processors), or other related components.

[0090] The term "computer system" can encompass all apparatus, devices, and machines for processing data, including, by way of example, a programmable processor, a computer, or multiple processors or computers. In addition to hardware, a processing system can include code that creates an environment for the execution of the computer program in question, such as code that constitutes processor firmware, a protocol stack, a database management system, an operating system, or a combination of one or more of these.

[0091] A computer program (also known as a program, software, software application, script, executable logic, or code) can be written in any form of programming language, including compiled or interpreted languages, or declarative or procedural languages, and can be deployed in any form, such as as a stand-alone program or as a module, component, subroutine, or other unit suitable for use in a computing environment. A computer program does not necessarily correspond to a file in a file system. A program can be stored as part of a file that holds other programs or data (e.g., one or more scripts stored in a markup language document), in a single file dedicated to the program in question, or in multiple coordinated files (e.g., a file that stores one or more modules, subprograms, or portions of code). A computer program can be deployed to be executed on one computer, or to be executed on multiple computers located at one site, or distributed across multiple sites and interconnected by a communication network.

[0092] Such implementations may include a set of computer instructions fixed on any tangible, non-transitory medium, such as a computer-readable medium. The set of computer instructions may embody all or part of the functionality previously described herein with respect to the system. Computer-readable media suitable for storing computer program instructions and data include, by way of example, all forms of non-volatile or volatile memory, media and memory devices, including semiconductor memory devices, such as EPROM, EEPROM, and flash memory devices; magnetic disks, such as internal hard disks or removable disks or magnetic tapes; magneto-optical disks; and CD-ROM and DVD-ROM disks. The processor and memory may be supplemented by, or incorporated in, special purpose logic circuitry. The components of the system may be interconnected by any form or medium of digital data communication, such as a communications network. Examples of communications networks include local area networks ("LANs") and wide area networks ("WANs"), such as the Internet.

[0093] Those skilled in the art should appreciate that such computer instructions can be written in a number of programming languages ​​for use with many computer architectures or operating systems. Furthermore, such instructions may be stored in any memory device, such as semiconductor, magnetic, optical, or other memory devices, and transmitted using any communications technology, such as optical, infrared, microwave, or other transmission technology.

[0094] Among other ways, such computer program products may be distributed as removable media (e.g., commercial software) accompanied by printed or electronic documentation, pre-installed on a computer system (e.g., on a system ROM or fixed disk), or distributed from a server or bulletin board over a network (e.g., the Internet or the World Wide Web). Indeed, some embodiments may be implemented in a Software-as-a-Service model ("SAAS") or a cloud computing model. Of course, some embodiments of the present disclosure may be implemented as a combination of both software (e.g., computer program products) and hardware. Still other embodiments of the present disclosure are implemented entirely as hardware or entirely as software.

[0095] One skilled in the art will readily appreciate that the present disclosure is well adapted to carry out the objects and obtain the ends and advantages mentioned, as well as those inherent therein. The disclosure described herein represents presently preferred embodiments, is exemplary, and is not intended as a limitation on the scope of the disclosure. Modifications and other uses within the scope of the disclosure, which are encompassed within the spirit of the disclosure as defined by the scope of the claims, will occur to those skilled in the art.

[0096] No admission is made that any reference, including non-patent or patent literature, cited herein constitutes prior art. In particular, unless otherwise stated, reference to any document herein is understood to be an admission that any of these documents form part of the common general knowledge in the art in the United States or any other country. Any discussion of a reference states what its author asserts, and applicants reserve the right to challenge the accuracy and pertinence of any of the documents cited herein. All references cited herein are incorporated by reference in their entirety unless expressly stated otherwise. The present disclosure shall control in the event of any discrepancy between definitions and / or explanations found in the cited references.

[0097] Examples of the present disclosure include: 1. A system for controlling turbulence in a fluid flow in a conduit, comprising: a conduit configured to have a fluid flow therethrough; at least one device associated with or integrated with the conduit and configured to generate disturbances in the fluid flow within the conduit to suppress calculated turbulent transition modes of the fluid flow; Including, the system. 2. The turbulence transition mode is based on a turbulence model that uses one or more properties of the conduit geometry and the fluid, and further includes determining at least one response function (R i (k)) and the excitation amplitude (u ki ) The system according to any of the embodiments herein, 3. A system as described in any of the Examples herein, wherein the turbulent transition mode is calculated according to Equation 12 and the generated disturbance is calculated as a function of Equation 4. 4. The system of any of the embodiments herein, wherein the conduit comprises a pipe or a channel. 5. At least the device includes an active flow disruption device, and the system comprises: a controller configured to command the active flow perturbation device; The active flow perturbation device is configured to modify a flow parameter of the fluid flow in the conduit in response to the controller; The system of any of the embodiments herein, wherein the controller is configured to generate commands based on the calculated turbulence transition mode.

[0098] 6. Further comprising at least one sensor configured to measure one or more characteristics of the fluid flow in the conduit related to a transition between laminar flow and turbulent flow; The system of any of the embodiments herein, wherein the controller is further configured to generate commands based on the measured characteristic. 7. A system described in any of the examples herein, wherein the controller is configured to at least one of calculate or adjust the calculation of a turbulent transition mode or an amplification response function of the turbulent transition mode of the fluid flow in the conduit based on the measured characteristics. 8. The system of any of the examples herein, wherein at least one device comprises an inner surface of a conduit. 9. A system as described in any of the examples herein, wherein the inner surface comprises a deformable material configured to absorb energy from calculated turbulent transition modes in the fluid flow. 10. A system as described in any of the examples herein, wherein at least one device includes a vibration inducing device arranged to introduce vibrational energy into the fluid flow to suppress the calculated turbulent transition modes.

[0099] 11. A method of controlling fluid flow in a conduit, comprising: The method includes adjusting a flow of the fluid through the conduit to reduce turbulence therein based on the determined turbulence transition mode. 12. Based on the turbulence model as a function of the geometry of the conduit and one or more properties of the fluid, and further according to the turbulence model, at least one response function (R i(k)) and the excitation amplitude (u ki The method of any of the examples herein, further comprising determining a turbulent transition mode by calculating 13. The method of any of the examples herein, further comprising calculating turbulence according to Equation 12 and calculating flow adjustment as a function of Equation 4. 14. The method of any of the examples herein, wherein adjusting the fluid flow includes selectively absorbing energy from the fluid at or near a calculated turbulent transition mode of the fluid flow. 15. A method according to any of the examples herein, wherein adjusting the fluid flow includes actuating an active flow control device configured to generate disturbances in the fluid flow in the conduit to suppress calculated turbulent transition modes of the fluid flow.

[0100] 16. A method as described in any of the examples herein, comprising regulating the flow of the fluid using at least one device associated with or integrated with the conduit, wherein regulating the flow of the fluid comprises introducing energy into or extracting energy from the fluid flow. 17. Sensing at least one characteristic of fluid flow in a conduit related to a transition between laminar flow and turbulent flow; adjusting the flow of the fluid with the at least one device based on the at least one sensed characteristic; The method of any of the Examples herein further comprising: 18. A method according to any of the examples herein, further comprising calculating or adjusting a calculation of a turbulent transition mode of the fluid flow in the conduit based on at least one sensed characteristic, and adjusting the fluid flow using the at least one device is further based on the calculated or adjusted turbulent transition mode. 19. A method according to any of the examples herein, comprising modifying a conduit by altering a characteristic of an inner surface of the conduit or associating at least one device with the conduit, wherein the at least one device or modified inner surface is configured to adjust fluid flow within the conduit to suppress calculated turbulent transition modes of the fluid flow. 20. A method of reducing turbulence in a fluid flow in a conduit, comprising: A method comprising: assuming a fluid flow through a conduit, generating disturbances in the fluid flow in the conduit to suppress calculated turbulent transition modes of the fluid flow.

[0101] 21. A turbulence control system for a conduit, the turbulence control system including at least one modification including at least one of an active, reactive, or passive turbulence control system configured to prevent, absorb, or suppress calculated turbulent transition modes of fluid flow in the conduit. 22. The turbulence control system of any of the examples herein, comprising at least one of: (a) a vibration inducing device configured to disturb the fluid flow in the conduit to suppress the calculated turbulent transition modes; (b) a textured surface disposed on the inner surface of the conduit; (c) a modified cross-section or cross-sectional configuration of the conduit; (d) a liner on the inner surface of the conduit configured to preferentially absorb energy from the fluid flow in the calculated turbulent transition modes; (e) a coating or surface finish on the inner surface of the conduit; or (f) conduit flexibility / deformation, wherein the one or more pipe modifications are configured to absorb or suppress the calculated turbulent transition modes of the fluid or gas in the pipe or channel. 23. A turbulence control system as described in any of the examples herein, wherein the conduit flexibility / deformation causes the pipe or material therein to absorb energy from transition modes of fluid or gas within the pipe or channel. 24. A turbulence control system as described in any of the examples herein, wherein the vibration inducing device is mounted on the inner or outer surface of the pipe or channel, or within the thickness of the wall of the conduit, to impart perturbations to the fluid or gas in the pipe or channel. 25. A turbulence control system as described in any of the examples herein, wherein the modification changes the flow-wise wavelength or cross-section of the pipe or channel such that the pipe or channel is mismatched with the occurrence of a transition mode of the fluid or gas in the conduit according to a predicted turbulent transition mode.

[0102] 26. A turbulence control system as described in any of the examples herein, wherein the modification includes a vibration absorbing material lining the inside of the pipe or channel, the vibration absorbing material being configured to preferentially absorb energy from the fluid flow in the conduit in a calculated turbulent transition mode. 27. A turbulence control system as described in any of the examples herein, further comprising an inspection gauge or tool for a pipe or channel configured to travel through an existing pipeline or channel line and retrofit the pipe or channel from within it by adding an active, passive, or reactive system for turbulence suppression of fluids or gases within the pipe or channel. 28. The turbulence control system of any of the examples herein, further comprising the manufacture of a new conduit integrated with the turbulence suppression system. 29. A turbulence suppression system as described in any of the examples herein, further comprising a construction site modification / retrofit of a pipe or channel for suppression of turbulent flow of a fluid or gas within the conduit.

[0103] The above-described embodiments of the present disclosure are intended to be merely illustrative, and numerous variations and modifications will be apparent to those skilled in the art. Those skilled in the art will appreciate further features and advantages of the present disclosure based on the above-described embodiments. Such variations and modifications are intended to be within the scope of the present invention, as defined by any of the appended claims. Thus, the present disclosure is not to be limited by what has been particularly shown and described, except as indicated by the appended claims. All publications and references cited herein are expressly incorporated herein by reference in their entirety.

[0104] [Embodiment] (1) A system for controlling turbulence in a fluid flow in a conduit, comprising: a conduit configured to have a fluid flow therethrough; at least one device associated with or integrated with the conduit and configured to generate disturbances in the fluid flow within the conduit to suppress calculated turbulent transition modes of the fluid flow; Including, the system. (2) The turbulence transition mode is determined based on a turbulence model using one or more properties of the conduit geometry and the fluid, and further includes determining at least one response function (R i (k)) and the excitation amplitude (u ki ) The system of embodiment 1, wherein the calculation is performed by: (3) The system of embodiment 2, wherein the turbulent transition mode is calculated according to Equation 12 and the generated disturbance is calculated as a function of Equation 4. (4) The system of embodiment 1, wherein the conduit comprises a pipe or a channel. (5) The at least one device includes an active flow disruption device, and the system further comprises: a controller configured to command the active flow perturbation device; the active flow perturbation device is configured to modify a flow parameter of the fluid flow in the conduit in response to the controller; 2. The system of claim 1, wherein the controller is configured to generate commands based on the calculated turbulence transition mode.

[0105] (6) further comprising at least one sensor configured to measure one or more characteristics of the fluid flow in the conduit related to the transition between laminar flow and turbulent flow; 6. The system of claim 5, wherein the controller is further configured to generate the command based on the measured characteristic. (7) The system of embodiment 6, wherein the controller is configured to at least one of calculate or adjust the calculation of the turbulent transition mode or an amplification response function of the turbulent transition mode of the fluid flow in the conduit based on the measured characteristics. (8) The system of embodiment 1, wherein the at least one device comprises an inner surface of the conduit. (9) The system of claim 1, wherein the inner surface comprises a deformable material configured to absorb energy from the calculated turbulent transition modes in the fluid flow. (10) The system of claim 1, wherein the at least one device includes a vibration inducing device positioned to introduce vibration energy into the fluid flow to suppress the calculated turbulent transition modes.

[0106] (11) A method for controlling fluid flow in a conduit, comprising the steps of: The method includes adjusting a flow of the fluid through the conduit to reduce turbulence therein based on the determined turbulence transition mode. (12) calculating at least one response function (R i (k)) and the excitation amplitude (u ki12. The method of claim 11, further comprising determining the turbulent transition mode by calculating 13. The method of claim 12, further comprising calculating the turbulence according to Equation 12 and calculating the adjustment of the flow as a function of Equation 4. 14. The method of claim 11, wherein adjusting the flow of the fluid includes selectively absorbing energy from the fluid at or near the calculated turbulent transition mode of the fluid flow. (15) The method of claim 11, wherein adjusting the flow of the fluid includes activating an active flow control device configured to generate disturbances in the fluid flow in the conduit to suppress calculated turbulent transition modes of the fluid flow.

[0107] (16) The method of embodiment 11, further comprising adjusting the flow of the fluid using at least one device associated with or integrated with the conduit, wherein adjusting the flow of the fluid comprises introducing energy into or extracting energy from the fluid flow. (17) sensing at least one characteristic of the fluid flow in the conduit related to the transition between laminar flow and turbulent flow; adjusting the flow of the fluid with the at least one device based on the sensed at least one characteristic; and 17. The method of embodiment 16, further comprising: (18) The method of embodiment 11, further comprising calculating or adjusting the calculation of the turbulent transition mode of the fluid flow in the conduit based on the sensed at least one characteristic, and adjusting the flow of the fluid using the at least one device is further based on the calculated or adjusted turbulent transition mode. (19) The method of embodiment 11, comprising modifying the conduit by changing a characteristic of an inner surface of the conduit or associating at least one device with the conduit, the at least one device or modified inner surface being configured to adjust the flow of the fluid within the conduit to suppress calculated turbulent transition modes of the fluid flow. (20) A method for reducing turbulence in a fluid flow in a conduit, comprising the steps of: 1. A method comprising: assuming a fluid flow through a conduit, generating disturbances in the fluid flow within the conduit to suppress calculated turbulent transition modes of the fluid flow.

Claims

1. 1. A system for controlling turbulence in a fluid flow in a conduit, comprising: a conduit configured to have a fluid flow therethrough; at least one device associated with or integrated with the conduit and configured to generate disturbances in the fluid flow within the conduit to suppress calculated turbulent transition modes of the fluid flow; Including, the system.

2. The turbulent transition mode is determined based on a turbulence model using the geometry of the conduit and one or more properties of the fluid, and further includes determining at least one response function (R ｉ (k)) and the excitation amplitude (u ｋｉ 2. The system of claim 1 , wherein the calculated value is determined by:

3. 3. The system of claim 2, wherein the turbulent transition modes are calculated according to Equation 12 and the generated disturbances are calculated as a function of Equation 4.

4. The system of claim 1 , wherein the conduit comprises a pipe or a channel.

5. The at least one device includes an active flow disruption device, and the system further comprises: a controller configured to command the active flow perturbation device; the active flow perturbation device is configured to modify a flow parameter of the fluid flow in the conduit in response to the controller; The system of claim 1 , wherein the controller is configured to generate commands based on the calculated turbulence transition mode.

6. and at least one sensor configured to measure one or more characteristics of the fluid flow in the conduit related to the transition between laminar flow and turbulent flow; The system of claim 5 , wherein the controller is further configured to generate the command based on the measured characteristic.

7. 7. The system of claim 6, wherein the controller is configured to at least one of calculate or adjust the calculation of the turbulent transition mode or an amplitude response function of the turbulent transition mode of the fluid flow in the conduit based on the measured characteristics.

8. The system of claim 1 , wherein the at least one device comprises an inner surface of the conduit.

9. The system of claim 1 , wherein the inner surface comprises a deformable material configured to absorb energy from the calculated turbulent transition modes in the fluid flow.

10. The system of claim 1 , wherein the at least one device comprises a vibration inducing device positioned to introduce vibrational energy into the fluid flow to suppress the calculated turbulent transition modes.

11. 1. A method for controlling fluid flow in a conduit, comprising: The method includes adjusting a flow of the fluid through the conduit to reduce turbulence therein based on the determined turbulence transition mode.

12. Based on a turbulence model as a function of the geometry of the conduit and one or more properties of the fluid, and further in accordance with the turbulence model, at least one response function (R ｉ (k)) and the excitation amplitude (u ｋｉ 12. The method of claim 11, further comprising determining the turbulent transition mode by calculating

13. The method of claim 12 further comprising calculating the turbulence according to Equation 12 and calculating the adjustment of the flow as a function of Equation 4.

14. The method of claim 11 , wherein adjusting the flow of the fluid comprises selectively absorbing energy from the fluid at or near the calculated turbulent transition mode of the fluid flow.

15. 12. The method of claim 11, wherein adjusting the flow of the fluid comprises actuating an active flow control device configured to generate disturbances in the fluid flow in the conduit to suppress calculated turbulent transition modes of the fluid flow.

16. 12. The method of claim 11, comprising adjusting the flow of the fluid with at least one device associated with or integrated with the conduit, and adjusting the flow of the fluid comprises introducing energy into or extracting energy from the fluid flow.

17. sensing at least one characteristic of the fluid flow in the conduit related to the transition between laminar flow and turbulent flow; adjusting the flow of the fluid with the at least one device based on the sensed at least one characteristic; and 20. The method of claim 16, further comprising:

18. 12. The method of claim 11, further comprising calculating or adjusting the calculation of the turbulent transition mode of the fluid flow in the conduit based on the sensed at least one characteristic, and adjusting the flow of the fluid using the at least one device is further based on the calculated or adjusted turbulent transition mode.

19. 12. The method of claim 11, comprising modifying the conduit by changing a characteristic of an inner surface of the conduit or associating at least one device with the conduit, the at least one device or modified inner surface configured to adjust the flow of the fluid within the conduit to suppress calculated turbulent transition modes of the fluid flow.

20. 1. A method for reducing turbulence in a fluid flow in a conduit, comprising:

1. A method comprising: assuming a fluid flow through a conduit, generating disturbances in the fluid flow within the conduit to suppress calculated turbulent transition modes of the fluid flow.

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